Camera Math Calculators

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Crop factor — full-frame-equivalent focal length and aperture for your lens

When you mount a 50 mm lens on an APS-C camera, it produces the same field of view as a 75 mm lens on full frame — because the smaller sensor captures only the center of the image circle. That ratio is the crop factor. Enter your focal length, aperture, and sensor format below and the calculator returns both the equivalent focal length and the equivalent aperture, with every constant shown and the exposure caveat explained up front.

DSLR & mirrorless · 5 sensor formats · All crop factors labeled
Exposure does not change Crop factor affects field of view and depth of field — it does not affect your exposure. An f/1.8 lens still meters and exposes as f/1.8 on any sensor. The "equivalent aperture" shown by this calculator describes depth-of-field equivalence only, not a correction you apply to your exposure settings.

The calculator

Crop factor equivalents for your lens

Change any input and the results update instantly. Select your sensor format to see the crop factor applied.

In millimeters — the number printed on your lens (e.g. 50, 85, 24).

The f-stop marked on your lens — e.g. 1.8, 2.8, 5.6, 11.

Each format has a fixed crop factor — see the reference table below.

How it works — the formulas in full

Two formulas. Both multiply by the crop factor. The distinction between them is important: one describes field of view, the other describes depth of field — and neither changes your exposure settings.

Variable definitions

What each symbol means

FL — focal length in millimeters, as printed on the lens.

N — the f-number (aperture). A dimensionless ratio: focal length divided by entrance-pupil diameter.

CF — crop factor. A dimensionless multiplier expressing how much smaller the sensor is compared to a 35 mm full-frame sensor. Full frame = 1.0; APS-C 1.5× = 1.5; Canon APS-C 1.6× = 1.6; Micro Four Thirds = 2.0; 1-inch = 2.7.

EFL — equivalent focal length. The focal length a full-frame lens would need to produce the same field of view.

EAP — equivalent aperture. The f-number a full-frame lens would need to produce the same depth of field and gather the same total light across the sensor area. This is a comparison value — it is not the f-number you dial in for exposure.

Equations

Crop factor constants (labeled) CROP_FULL_FRAME = 1.0 // 35 mm full frame — the reference CROP_APS_C_1_5 = 1.5 // Nikon, Sony, Fuji APS-C CROP_CANON_APS_C = 1.6 // Canon APS-C (slightly smaller sensor) CROP_MICRO_4_3 = 2.0 // Micro Four Thirds (Olympus, Panasonic) CROP_ONE_INCH = 2.7 // 1-inch sensor (Sony RX100, Nikon CX, etc.)
Formula 1 — Full-frame-equivalent focal length EFL = FL × CF

Multiply your lens focal length by the crop factor. A 50 mm lens on APS-C 1.5× gives EFL = 50 × 1.5 = 75 mm. This describes field of view — how zoomed-in the image looks compared to a full-frame shot. The lens focal length does not physically change.

Formula 2 — Equivalent aperture (depth of field & total light — NOT exposure) EAP = N × CF

Multiply your f-number by the crop factor. A 50 mm f/1.8 lens on APS-C 1.5× gives EAP = 1.8 × 1.5 = f/2.7. This tells you: to match the depth of field you get from this APS-C setup on a full-frame camera, you would need a 75 mm f/2.7 lens.

Critical: your f/1.8 lens still exposes exactly as f/1.8 on the APS-C body. Do not apply the equivalent aperture to your metering, shutter speed, or ISO. Crop factor does not change the amount of light reaching each pixel — it changes how much of the image circle the sensor captures.

Crop factor constants — the full reference

These are the fixed constants this calculator uses. The crop factor for each format is derived from the ratio of the 35 mm full-frame diagonal (43.3 mm) to the sensor's diagonal. The active row is highlighted when you select a format above.

Sensor format Crop factor Sensor diagonal (approx.) 50 mm becomes f/1.8 DoF equiv.
Full frame (35 mm) 1.0× 43.3 mm 50 mm f/1.8
APS-C 1.5× (Nikon, Sony, Fuji) 1.5× 28.4 mm 75 mm f/2.7
Canon APS-C 1.6× 1.6× 26.7 mm 80 mm f/2.9
Micro Four Thirds 2× 2.0× 21.6 mm 100 mm f/3.6
1-inch sensor 2.7× 2.7× 15.9 mm 135 mm f/4.9

The "f/1.8 DoF equiv." column shows the equivalent aperture for a physical f/1.8 lens on each format — this is for depth-of-field comparison only. Your exposure remains f/1.8 regardless of sensor format. Sensor diagonals are approximate; crop factors are conventional rounded values used across the industry.

Worked example — step by step

A 50 mm lens at f/1.8 on an APS-C 1.5× camera. These match the calculator's default inputs — every figure below can be verified by hand in seconds.

Inputs

50 mm · f/1.8 · APS-C 1.5×

FL = 50 mm  |  N = 1.8  |  CF = 1.5 (APS-C 1.5×)

Step 1 — Identify the crop factor

The sensor is APS-C 1.5× (Nikon, Sony, or Fuji body). From the constants table:
CF = 1.5 — this sensor is 1.5× smaller than full frame in linear dimension.

Step 2 — Equivalent focal length

EFL = FL × CF
EFL = 50 × 1.5
EFL = 75 mm

A 50 mm lens on this APS-C body frames a scene identically to a 75 mm lens on full frame. The lens has not changed; the sensor is cropping the image circle.

Step 3 — Equivalent aperture (depth of field comparison only)

EAP = N × CF
EAP = 1.8 × 1.5
EAP = f/2.7

To produce the same depth of field as this APS-C f/1.8 setup on a full-frame camera, you would need a 75 mm lens set to f/2.7. The APS-C sensor's smaller size means it has inherently more depth of field for the same field of view.

Step 4 — Confirm your actual exposure is unchanged

The f/1.8 lens is still f/1.8 for metering purposes. Your camera meters at f/1.8, your shutter speed and ISO reflect f/1.8 — nothing about the exposure calculation changes. The equivalent aperture f/2.7 is a system-comparison number used when evaluating how this APS-C kit compares to a full-frame kit for background blur or low-light depth-of-field control. It is not a value you enter into your camera.

Step 5 — Interpret the results

A 50 mm f/1.8 on APS-C 1.5× is equivalent in framing to a 75 mm f/2.7 on full frame. That means: you get the field of view of a short telephoto but with more depth of field than a full-frame shooter using the same framing. Background blur will be less pronounced than a true 75 mm f/1.8 full-frame setup — a common source of confusion for photographers moving between systems.

Common mistakes with crop factor

Crop factor is a simple multiplication, but the surrounding concepts trip up even experienced photographers. These are the errors that show up most often.

Thinking the lens physically changes or "zooms in"

The lens does not change when mounted on a smaller sensor. Its focal length, aperture, and optical characteristics are fixed. What changes is the field of view recorded by the sensor — a smaller sensor captures a smaller area from the center of the image circle, which looks like a crop of the full-frame image. The phrase "acts like a 75 mm lens" is shorthand for field of view only; the glass behaves exactly as a 50 mm lens at all times.

Applying the equivalent aperture to exposure settings

The equivalent aperture (f-number × crop factor) is a depth-of-field comparison value. It is not a correction to make to your camera. If you shoot f/1.8 and then set your camera to f/2.7 because of the "equivalent aperture," you will underexpose by over a full stop. Your metering, shutter speed, and ISO should always reflect the actual f-number on your lens, which in this case is f/1.8.

Forgetting that the sensor crops, not magnifies

A common mental model is that a crop sensor "magnifies" the image — this is not quite right. The lens projects the same image circle it always projects. The crop sensor simply records a smaller portion of it. The effect on field of view is the same as cropping in post-processing and enlarging — you see less of the scene, but the physics of the lens have not changed. Understanding this distinction helps when thinking about resolution: a crop sensor captures fewer pixels from the lens's full image circle.

Using the wrong crop factor for Canon vs. other APS-C bodies

Not all APS-C sensors are identical. Most manufacturers (Nikon, Sony, Fuji) use a 1.5× crop factor, but Canon APS-C sensors are slightly smaller and use 1.6×. The practical difference is small — a 50 mm lens becomes 75 mm on a Nikon APS-C body and 80 mm on a Canon APS-C body — but when shooting at the edge of a focal length for a specific purpose (shooting sports at a 400 mm threshold, for example), the 6% gap matters. Always check which body you are working with.

Expecting the same background blur as a full-frame equivalent focal length

A 50 mm f/1.8 on APS-C gives the field of view of 75 mm but not the background blur of 75 mm f/1.8 on full frame. The depth of field is equivalent to a 75 mm f/2.7 full-frame setup — noticeably more depth of field, noticeably less background separation. Photographers who switch from full frame to a crop system expecting the same subject isolation are often disappointed. Use the equivalent aperture value to set realistic expectations before choosing a system or a lens.

Frequently asked

Crop factor is a number that describes how much smaller a camera sensor is compared to a 35 mm full-frame sensor. A sensor with a crop factor of 1.5 has a sensor area small enough that it captures only the center portion of the image circle a full-frame lens projects. The result is that objects appear larger in the frame — the same visual effect as zooming in — which is why a 50 mm lens "acts like" a 75 mm lens on an APS-C 1.5× camera. The sensor is not magnifying the image; it is simply capturing a smaller crop of the same optical image.
No. Crop factor does not change your exposure. An f/1.8 lens meters and exposes as f/1.8 regardless of which sensor it is mounted on. Your shutter speed, ISO, and the brightness of a scene are entirely unaffected by the sensor size. The "equivalent aperture" this calculator shows describes depth-of-field equivalence and total-light equivalence when comparing two systems that produce the same framing — it is a comparison tool, not an exposure correction. Always set your exposure based on the f-number marked on the lens.
No. The lens does not change at all. Its focal length remains exactly as marked, and its optical behavior is unchanged. What changes is the portion of the image circle that the sensor records. Because the smaller sensor covers only the center of the image circle, subjects fill more of the frame — producing the same visual result as a longer focal length on full frame. The phrase "acts like a 75 mm lens" is shorthand for "produces the same field of view as a 75 mm full-frame lens," not a description of any physical change to the optics.
Equivalent aperture matters for two reasons: depth of field and total light gathered across the sensor area (which affects noise and dynamic range in system comparisons). A 50 mm f/1.8 on APS-C 1.5× gives the same field of view as a 75 mm on full frame, but it does not give the same shallow depth of field or the same total photon count across the sensor. To match the depth of field of a 75 mm f/2.7 full-frame lens, you would need to use f/2.7 on full frame — not f/1.8. The equivalent aperture tells you precisely where the two systems diverge when comparing background blur and low-light depth-of-field control.
Most APS-C sensors use a crop factor of 1.5× — this covers Nikon (DX), Sony E-mount APS-C, and Fuji X bodies. Canon APS-C sensors are slightly smaller and use a crop factor of 1.6×. The practical difference is small: a 50 mm lens becomes 75 mm equivalent on a Nikon or Sony APS-C body, and 80 mm equivalent on a Canon APS-C body. Micro Four Thirds sensors use 2.0×, and 1-inch sensors (used in Sony RX100 and Nikon CX series) use approximately 2.7×. This calculator uses the conventional rounded values for each format.
Yes, with the correct mount adapter or native compatibility. Full-frame lenses project an image circle large enough to cover a full-frame sensor, so they more than cover a crop sensor with room to spare. The crop factor applies to the effective field of view: a 24 mm wide-angle full-frame lens becomes a 36 mm equivalent on APS-C 1.5×, losing most of its wide-angle character. Lenses designed specifically for crop sensors (labeled APS-C, DX, EF-S, etc.) project a smaller image circle optimized for the smaller sensor and typically cannot cover a full-frame sensor without heavy vignetting in the corners.